Tunneling device

ABSTRACT

A method and apparatus to analyze the aerial image of an optical system using a subwavelength slit. A slit configuration yields a higher signal-to-noise ratio than that achievable with a round aperture. The slit also allows the polarization of the aerial image to be analyzed. In an alternative embodiment a tunneling slit is used. The tunneling slit comprises an optically transparent ridge-like structure mounted to a substrate, the combined structure covered by a thin, planar metal film.

This is a Division of application No. 08/209,026, filed Mar. 9, 1994,now U.S. Pat. No. 5,631,731.

BACKGROUND OF THE INVENTION

The present invention relates generally to self metrology of opticalprojection lithography systems, and more specifically, to a method andapparatus for analyzing the aerial image of such a system using asubwavelength slit.

As the feature sizes on integrated circuit devices have grown eversmaller, the demands on the optical train in the optical lithographysystem have grown ever greater. This has led to an increased need fortechniques for accurate and real-time monitoring of the optical system'sperformance.

In a typical prior art technique for monitoring system performance, areticle pattern is imaged onto a resist coated substrate. The substrateis then developed and used to analyze the optical system's performance.The analysis is based on the pattern being a convolution of a perfectimage of the reticle and the performance characteristics of thestepper's optical system. Unfortunately, the nonlinear qualities of thephotoresist technique adds a third variable making it difficult toaccurately reduce the data and derive the performance of the opticalsystem. A further problem with this method of analysis is that it isslow and time consuming.

SUMMARY OF THE INVENTION

The invention provides a method and apparatus for analyzing the aerialimage of an optical system using a subwavelength slit (a slit narrowerthan the wavelength of the light illuminating it) or its functionalequivalent. The aerial image refers to the intensity distribution of animage in or near the image focal plane of an optical system. Analysis ofthis image, especially in systems operating near the diffraction limitsof the optical system, provides valuable real-time information on theperformance of the optical system.

A slit is used instead of a round aperture in order to increase theamount of energy transmitted beyond the slit. Subwavelength roundapertures in metal films of finite thickness transmit essentially onlyevanescent light. Evanescent light refers to electromagnetic fieldsproduced in the immediate vicinity of the aperture edges. These fieldsdon't propagate like normal electromagnetic waves and therefore cannotbe detected remotely. However, if a dielectric medium is present, somefraction of the evanescent light is converted to propagating waves whichcan be detected. Although a slit also produces evanescent light, forincident light with the magnetic vector parallel to the slit edge apropagating mode always exists, which produces a substantial increase inthe slit's transmission.

In the preferred embodiment, a slit plate is included on the waferholder stage of an optical projection lithography system. In order toexamine the aerial image of the optical system prior to exposing thewafer, the stage is repositioned such that the slit plate will lieproximate to the image plane of the optical system. After replacing thereticle with a special test pattern, the slit is scanned across theimage plane while the transmission of the slit is monitored. Thisprovides the user with a high resolution intensity profile of thegenerated image. In the preferred embodiment, a fluorescent materialmounted in the near field of the slit converts transmitted light,including evanescent light, to longer wavelengths which are subsequentlydetected by a photodetector. From the intensity profile of the aerialimage, errors in the optical system can be determined. Thus this systemoffers a real time, high fidelity method of monitoring the performanceof the optical system.

The aerial image most readily analyzed by the slit is a line image,oriented parallel to the slit long axis, and longer than the slitlength. The slit plate preferably includes slits with severalorientations, so that line patterns with different orientations can beanalyzed. The slits and their corresponding patterns are positioned sothat only the slit, or slits, of a given orientation are illuminated ata given time.

In an alternative embodiment, a tunneling slit is used instead of thesubwavelength slit. The tunneling slit, a functional equivalent to thesubwavelength slit, has no actual slit or interruption in its surface.It is designed and fabricated to have transmission characteristicssimilar to those of a subwavelength slit. The tunneling slit ispotentially easier to fabricate then the subwavelength slit and yetprovides comparable performance.

In an alternative embodiment, the aerial image consisting of a parallelseries of images is analyzed using a series of parallel slits with thesame spacing as the image periodicity. In this embodiment the slits caneither be subwavelength slits or tunneling slits. Due to the multipleslit arrangement, the intensity is increased as is the signal-to-noiseratio.

Studies show a 150 nm wide slit of molybdenum (Mo) or silicon (Si) withvertical walls and thickness of about 120 nm can represent close to anideal aerial image monitor. This slit reproduces the width of the aerialimage to within about 5% for both transverse electric mode (TEM) andtransverse magnetic mode (TMM) polarization states. Furthermore thetransmissions for TEM and TMM agree to within about 5%. The imagecontrast determined by the slit is in good agreement with that of theaerial image. From signal to noise considerations it should be possibleto measure an image in less than 1 sec using a single slit 10 μm long.

A subwavelength slit for use with the present invention may befabricated with vertical sidewalls (sometimes referred to as a standardslit) or sloping sidewalls (sometimes referred to as a vee slit).Vertical walled slits can be fabricated using electron-beam lithography.However, vee-shaped slits and tunneling slits can be fabricated fromsilicon (Si) using optical lithographic techniques.

Reference to the remaining portions of the specification and thedrawings will provide further understanding of the nature and advantagesof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows an optical projection lithography stepper system utilizingthe aerial image analyzer of the present invention;

FIG. 1B shows the use of one embodiment of the present invention as ameans of measuring the optical performance of the stepper;

FIG. 2 shows one example of a special test pattern;

FIG. 3A shows the simultaneous examination of several parallel lineimages;

FIG. 3B shows an alternative embodiment utilizing a light pipe and aphotomultiplier;

FIG. 4 shows the analytical waveguide model;

FIG. 5 shows a series of plots of transmission versus film thickness forslits in which the slit walls are parallel and vertical;

FIGS. 6A-6C show other slit geometries;

FIG. 7 shows a series of plots of transmission versus film thickness forvee geometry slits with 50, 100, and 200 nm slit widths;

FIG. 8 shows a series of plots of transmission versus film thickness forinverted vee geometry slits with 50, 100, and 200 nm slit widths;

FIG. 9 shows the signal-to-background ratio versus film thickness for50, 100, and 200 nm slit widths;

FIG. 10 shows the fraction of TM polarization in the transmitted signalfor the vertical side wall case;

FIG. 11 shows the degree of TM polarization versus film thickness forthe vee slit geometry;

FIG. 12 shows the TM polarization versus slit width for the vee slitgeometry;

FIG. 13 shows the modulation transfer function (MTF) for a vee geometryslit with a Mo film thickness of 120 nm and slit widths of 50, 100, and200 nm;

FIG. 14 shows conditions in which the TE and TM MTF's are almost thesame;

FIG. 15 shows the transmitted power from a slit, assuming a slit lengthof 10 μm and an illumination intensity of 100 mW per square centimeter;

FIG. 16 shows the calculated signal-to-noise ratio (S/N);

FIG. 17 shows the tunneling slit;

FIG. 18A, 18B, and 18C show the preferred fabrication techniques for thetunneling slit.

FIG. 19A shows the calculated transmission through a parabolic tunnelingslit;

FIG. 19B shows the dimensional variables used in FIG. 19A;

FIG. 20A shows the calculated transmission through a triangular (or"inverted vee") tunneling slit;

FIG. 20B shows the dimensional variables used in FIG. 20A; and

FIG. 21 shows the MTF's for tunneling slits.

DESCRIPTION OF SPECIFIC EMBODIMENTS

System Overview

FIG. 1A shows an optical stepper lithography system 10. In a typicalchip processing configuration, a light source 12 and optics 14 image areticle 15 onto a wafer 17. Wafer 17 is mounted to an x-y-z positioningstage 18. Stage 18 allows step and repeat patterns to be applied towafer 17. Also mounted to stage 18 is a slit plate 11 which, in thisembodiment, contains several slits 13, each oriented in a differentdirection. A rectilinear coordinate system 20 is denoted schematically.

FIG. 1B shows the use of one embodiment of the present invention as ameans of measuring the optical performance of modified stepper 10. As inthe prior art technique, reticle 15 is replaced with a special testpattern (step 30). Stage 18 is translated until wafer 17 is replacedwith subwavelength slit 13 or its functional equivalent (step 32). Inthis position the slit is lying in, or within a few wavelengths of, theimage plane. The slit is then moved or scanned across the image plane,the long axis of the slit being held perpendicular to the scan direction(step 34). During the scanning operation, the intensity of the slit'stransmission is monitored and recorded (step 35). The measured intensityprofile is compared to a previously calculated profile expected from a"perfect" stepper (step 36). From this comparison the performancecharacteristics of the optical system are determined (step 38).

FIG. 2 shows one example of a test pattern. Several sets of linepatterns, at different orientations to the stepper's x-y coordinatesystem, are positioned in different regions of the image field of thestepper optics. Such a pattern should allow the image quality to be wellcharacterized over the entire image field and allow the separatedetermination of a number of basic lens aberrations, such as sphericalaberration, coma, and astigmatism. Additional sets of line patterns ofdifferent line width can provide additional information, which can beused to optimize exposure conditions. The present invention thereforeoffers the advantage of being able to perform real time, high fidelityanalysis of the performance of the optical system.

FIG. 3A shows the simultaneous examination of several parallel aerialline images 41. Instead of a single slit being used, multiple slits 42are used, thereby increasing the signal level. The period of the slitsshould be either equal to or a multiple of the period of the aerialimage to be analyzed in order to achieve the desired higher signallevels. The long axes of all of the slits 42 are held perpendicular tothe scan direction. In this embodiment, a fluorescent material 45 ismounted within the near field of slits 42. Material 45 converts thelight to longer wavelengths where it is detected by a photodetector 46.The use of fluorescence has the advantage that it is easier to detectlight in the longer wavelengths. FIG. 3B shows an alternative embodimentin which fluorescent material 45 and detector 46 are replaced with alight pipe 47 which transmits the photons to a photomultiplier 48.

Slit Characteristics

FIG. 4 shows an example of the analytic waveguide model used to analyzethe behavior of various slit designs. The slit is treated like awaveguide in the z direction (normal to the plane of the film). If theslit dimensions vary with z, several waveguide sections or `slabs` 51,one above the other and of varying sizes to match the z dependence, areused.

For each slab 51 the eigenfunctions are calculated. Polarization effectsand evanescent light are included. For an incident plane wave, boundaryconditions at the interfaces between the slabs, the substrate, and theair are matched to obtain eigenvalues for all slab eigenfunctions. Forconducting slabs the eigenvalues are complex. Next the S-matrix whichcouples the incident plane wave to the transmitted wave is calculated.The S-matrix completely defines the transmission properties of the slitstructure. For an aerial image, the image is Fourier transformed intoplane wave components. Then the S-matrix is applied to transmit thesecomponents through the slit where they are recombined to give thetransmitted amplitude and intensity. Because the above analysis uses agrating equation formalism in its calculations, a set or array of slitsis assumed in all calculations. A repeat distance 52 of 2 μm is used.

FIG. 5 shows a series of plots of transmission versus film thickness forslits in which the slit walls are parallel and vertical. The definitionof transmission here requires some explanation. Normally transmissionwould be defined as the fraction of light incident on the slit which istransmitted. The transmitted power/unit length is then proportional tothe slit width and the transmission coefficient. However, transmissionis defined here as the fraction of light incident over one repeatdistance which is transmitted, to allow the effects of the partialtransparency of very thin films to be included.

In the preferred embodiment, the slit is fabricated using standardmicro-circuit processing techniques which are well known in the art. Theslit film sits on top of a dielectric substrate representing thefluorescent converter which, in the preferred embodiment, is made ofCaF₂. The index of refraction is taken as 1.468. The presence of thesubstrate has some effect on the transmission. Slit films of both chrome(Cr) and Mo are analyzed for slit widths of 50, 100, and 200 nm, each.Mo and Si have almost identical optical constants and therefore can beexpected to perform similarly. Slits fabricated from Si, however, shouldbe much easier to make than those of Mo.

As shown in FIG. 5, in most cases for small metal film thickness thetransmission through the slits in the real metal films exceeds that forthe perfectly conducting case. This is because of the tunneling of lightthrough the film which is significant for thin films. The effect is lessfor the Mo films, because the extinction factor of Mo is about twicethat of Cr.

FIGS. 6A-C show other slit geometries. A slit 71 is a `standard` slit inwhich the slit walls 72 are vertical and parallel to the optic axis 73.A slit 74 has a `vee` geometry while slit 75 has an `inverted vee`geometry. The angles between the slit walls and optic axis 73 for bothslits 74 and 75 are 45 degrees, but other angles (say 30-60 degrees) canbe used. Arrow 76 indicates the direction of the light incident on theslits. A material 77 indicates the slit substrates. Creating either thevee slit 74 or the inverted vee slit 75 in metal would probably bedifficult, but they can be made in a straightforward way using singlecrystal Si in the <100> orientation, and anisotropic etching. However,the angle between the slit wall and the optic axis would then be 35.26°.These structures are modeled by approximating the sloping edges by aseries of rectangles/slabs whose horizontal dimensions change in aregular manner.

FIG. 7 shows a series of plots of transmission versus film thickness forvee geometry slits with 50, 100, and 200 nm slit widths. Thetransmission dependence on metal thickness is more complicated than thecase with vertical walls. Also there is less decrease in transmissionwith increasing metal thickness than for the vertical wall case. To someextent the higher transmission is probably due to the thinner walls nearthe vee, so that this slit behaves like a vertical wall slit with alarger opening. There may be a collection horn effect as well, with thesloping walls allowing a better impedance match between free space andthe interior of the slit.

FIG. 8 shows a series of plots of transmission versus film thickness forinverted vee geometry slits with 50, 100, and 200 nm slit widths. Likethe vee geometry there is less decrease with increasing metal thicknessthan for the vertical wall case. However the variations in transmissionwith metal thickness are smaller than the vee case.

FIG. 9 shows the signal-to-background ratio (s/b) for a slit withvertical walls scanning a line pattern which is assumed to be as long asthe slit, and with uniform illumination extending over a distance of 0.5μm normal to the slit edge. In this case, the signal is the light goingthrough the slit while the background is the light tunneling through themetal film. An acceptable s/b value is one in which the background hasno significant effect on the measurements even when the slit is set nearthe edge of the image where the illumination is reduced. Furthermorethere may be several line images or patterns illuminating the metal filmfor a single slit, so the results in FIG. 9 may represent anunderestimate of the background by as much as a factor of 10. Thereforea reasonable value for s/b may be in excess of 10₄. The required minimumthicknesses of the films are then about 60 to 70 nm for Mo and about 120to 130 nm for Cr.

The incident polarization can always be decomposed into components ofTransverse Magnetic mode (TM-magnetic vector parallel to the sides ofthe slit) and Transverse Electric mode (TE-electric vector parallel tothe sides of the slit). Theoretically, at least one TM mode can alwayspropagate through even a very narrow slit, i.e., it doesn't decayexponentially with the thickness of the slit material. This is animportant advantage of the slit over a round aperture. Polarizationeffects are becoming important in lithography systems with highnumerical aperture (NA) lenses, therefore an aerial image sensor whichcan measure polarization may be desirable. Furthermore, because theaerial image is measured in air rather than resist, the polarizationeffects are larger since the NA is reduced in the resist by its index ofrefraction.

FIG. 10 shows the fraction of TM polarization in the transmitted signalfor the vertical side wall slit case. For smaller width slits thepolarization can be 100 percent TM for film thicknesses consistent withthe S/B requirements shown in FIG. 9. Note that if a non-polarizingsensor were desired, a slit width between 100 and 200 nm would berequired.

FIGS. 11 and 12 show the result of calculations for the vee slitgeometry. FIG. 11 shows the degree of TM polarization versus filmthickness while FIG. 12 shows the TM polarization versus slit width fora Mo slit with the vee slit geometry. Very high degrees of TMpolarization appear possible for this geometry. It also appears possibleto get a TM polarization of 0.5 (corresponding to no polarization) for aslit width of about 60 nm and a metal thickness of 120 nm. The aboveanalysis assumes normally incident waves. However, the results arelittle changed if light converging from a finite NA is used instead.

FIG. 13 shows the modulation transfer function (MTF) for a vee geometryslit with a Mo film thickness of 120 nm and various slit widths. The MTFdefinition for a slit is completely analogous to the normal definitionof the MTF for a lens system in optics. The analysis is based on anormally incident plane wave and two other plane waves which areincident at angles (±θ). The amplitude (to within a phase factor) at thesurface of the film is 1+cos (2πf_(T) x) where f_(T) =sin θ/λ is thetransverse spatial frequency. The transmitted signal from thisilluminated sinusoidal grating is calculated for values of 2πf_(T) x=0and 2πf_(T) x=π, at which the signal amplitudes are maximum (2) andminimum (0). This is equivalent to scanning the slit across thesinusoidal pattern. If the transmitted signal is I(2πf_(T) x) thecontrast C can be defined as C=(I(0)-I(π))/(I(0)+I(π)).

The value of C depends on f_(T). For small values of f_(T), i.e., verylong transverse periods, the slit will follow the intensity variationvery closely and the contrast will be .sub.˜ 1. However, as f_(T)increases, the contrast will drop. The maximum value of f_(T) is 1/λwhere λ is the wavelength of the light. The slit must be at least lessthan λ in order to pass all the spatial frequency components of theincident wave. For a coherent image produced by a lens with numericalaperture NA, the maximum spatial frequency is NA/λ. In addition thecontrast for the components must be high enough that noise doesn'tdegrade the signal.

Since the MTF will in general depend on slit width, film thickness, andfilm composition, there is a considerable range of properties to beexplored. Shown for comparison in the figure are the MTF's for anaberration free lens with an NA =0.6, illuminated by purely coherent orincoherent light. The slit MTF's extend to higher spatial frequenciesthan in the coherent case, and exceed the modulation level of theincoherent case. A line/space pattern illuminated with partiallycoherent light will lie between the coherent and incoherent lines.Therefore it is likely the slit will pass all the spatial frequencies ofsignificance in the aerial image. However the higher frequency featureswill be reduced, because the slit MTF is less than 1.0. Therefore acorrection process may be needed. For purely coherent or incoherentillumination the correction process can consist of Fourier transformingthe scanned image, dividing the frequency spectrum by the slit MTF, andFourier transforming back. For spatial frequencies where the projectionlens MTF is small, this correction process does not have to be veryaccurate.

FIG. 13 also shows that the MTF is different for TE and TM modes forthis particular case. This is related to differences in transmission ofthe two modes described above. FIG. 14 shows a situation where the TEand TM MTF's are almost the same. For this example, a vee slit with a 65nm slit width in Mo with a metal thickness of 120 nm is used (see FIG.12). As will be seen below, a 150 nm vertical wall slit will have theMTF's approximately the same for TE and TM modes, and thus create nopolarization effects.

The fact that the slit behavior is sensitive to polarization fornarrower slit widths suggests that there is a trade-off betweenresolution and polarization insensitivity. Polarization sensitivity isno problem, however, if its effects can be measured. This can be done bymeasuring the aerial image sequentially with two slits with differentpolarization dependencies. The TE and TM images can then be determined.These slits may not have the same MTF, but as long as it is possible tocorrect for the effects of an MTF which is less than 1, there should notbe a problem.

First consider the case where the polarization dependence isapproximately independent of the spatial frequency composition of theimage. Then the image is scanned with slits 1 and 2, the scannedintensities I₁ (x)≡I₁ and I₂ (x)≡I₂ can be written in terms of the TMand TE polarization components of the aerial image as

    I.sub.1 =ε.sub.TE.sup.1 I.sub.TE +ε.sub.TM.sup.1 I.sub.TM

    I.sub.2 =ε.sub.TE.sup.2 I.sub.TE +ε.sub.TM.sup.2 I.sub.TM

where ε¹ _(TE), ε¹ _(TM), ε² _(TE), and ε² _(TM) are the polarizationdependent transmissions for slits 1 and 2. The intensities for the twopolarization states I_(TE) and I_(TM) are obtained by solving the abovetwo equations for them.

When the polarization dependence varies with the spatial frequency f thederivation is as follows for the case of coherent illumination. TheFourier transforms of the measured intensities, I₁ (f) and I₂ (f), canbe written in terms of the TE and TM components of the frequency spectraof the aerial image and the MTF's for the two polarization components ofthe two slits:

    I.sub.1 (f)=MTF.sub.TE.sup.1 (f)I.sub.TE (f)+MTF.sub.TM.sup.1 (f)I.sub.TM (f)

    I.sub.2 (f)=MTF.sub.TE.sup.2 (f)I.sub.TE (f)+MTF.sub.TM.sup.2 (f)I.sub.TM (f).

Solving for I_(TE) (f) and I_(TM) (f), and taking the Fourier transformyields the aerial images for the two polarization states I_(TE) (X) andI_(TM) (x) . Some error may be introduced by these operations. However,if the spatial frequency dependencies of the two polarization states arenot too different, the error will be small.

For the case of partial coherence, the MTF cannot be defined in general.However, for a specific pattern, such as the line patterns describedabove, a quantity which behaves like the MTF can be defined. Thus,relations similar to the above equations can be written, and theseequations can then be solved for I_(TE) and I_(TM).

FIG. 15 shows the transmitted power from a slit, assuming a slit lengthof 10 μm and an illumination intensity of 100 mW per square centimeter.The signal levels are approximately 10⁻¹⁰ to 10⁻⁹ watts.

FIG. 16 gives the calculated signal-to-noise ratio (S/N) based on anumber of assumptions. A collection efficiency of 30 percent was used. Adetector response to 248 nm photons was used. A photomultiplier with aquantum efficiency of 20 percent and a gain of 10⁶ followed by apreamplifier with an input noise factor of 2.2×10⁻¹¹ amps for afrequency bandwidth of 1000 hertz and at a sensitivity of 100 nanoampsper volt was assumed. Very high values of S/N are possible with theslits.

Tunneling Slit and Dot Structures

FIG. 17 illustrates a tunneling slit structure according to one aspectof the present invention. Light is incident on the top surface from adirection 190. A ridge-like optically transparent structure 191 ismounted on the surface of the fluorescent detector 192. Note that inthis embodiment substrate 192 is actually serving two functions: first,as a substrate onto which the ridge is mounted and second, as anintegral part of the detector. Alternatively the fluorescent detectormay simply be a light pipe which transmits 248 nm photons to a deepultraviolet sensitive detector like a photomultiplier. In an alternativeembodiment, the ridge-like structure can be made of a fluorescentmaterial.

The structure is covered by a planar metal film 193, such that only avery thin layer of metal 194 covers the highest part of the ridge. Thismakes it possible for light to tunnel through the thinnest parts of thefilm. Because the tunneling decreases exponentially with the thicknessof the metal, the transmission is limited to the very thinnest layers.Therefore, it is possible to achieve high resolution with this devicewithout having to create structures as narrow as the desired resolution.

FIG. 18A is a flow diagram of the preferred fabrication technique forthe tunneling slit. FIG. 18B shows pictorially the results at variousstages of the fabrication. While the drawing shows a single tunnelingslit, the technique is typically carried out to produce a plurality oftunneling slits. The slits can be spaced by a desired spacing to providea multiple-slit structure along the lines of those shown in FIGS. 3A and3B, or can be spaced farther apart to allow several single-slitstructures to be fabricated.

First, a substrate is coated with a relatively thick layer of positivephotoresist (step 205). Using conventional lithography techniques, thephotoresist is exposed through a reticle which projects a narrow line,or lines, typically less than or equal to about 1 μm wide (typicallyapproximately 0.5 μm wide) and 5 μm or more in length (typically 10 to20 μm long) (step 210). A trench-like structure is left in the resistcoated substrate after developing the photoresist (step 215). Next, anoptically transparent material is deposited on the substrate therebyfilling the trench (step 220). Once the resist is stripped away (step225), the substrate is left with the deposited dielectric ridge. Anumber of different techniques can be used to round off the ridge (step230) including thermal annealing, reactive ion etching, and chemicaletching. After the ridge has been properly shaped, a metal film isdeposited (step 240). The metal film is subsequently planarized andthinned, preferably using an etching technique, until the metalthickness measured at the highest portion of the ridge is much less thanthe applicable design wavelength (step 250).

FIG. 18C shows pictorially the results at various stages according to analternative fabrication technique, which is capable of providing furthersimplification in fabrication. FIG. 18C illustrates the followingdescription. Using semiconductor processing techniques similar to thosedescribed above in FIG. 18B (i.e., steps 205-230), an array of theridges is constructed on a substrate. In this case the material need notbe optically transparent. A very thin layer of silver is sputtered on,and then a thick layer of nickel is applied by immersion in a nickelbath. The thick metal film is then separated from the substrate andridge structure. This metal film can then serve as a "master" to makeadditional tunneling slit structures, by compression molding, injectionmolding, or photo polymerization. It is possible to mold glass as wellas plastics. The result is an array of transparent ridges integrallyformed on a transparent substrate. Thereafter, a metal film is depositedand planarized as described above (i.e., steps 240 and 250). The processof molding the ridges is essentially identical to that used in makingoptical compact disks. The features on these disks are submicron indepth and size; thus it is likely this process can be used, and couldreduce the cost of the tunneling slits significantly.

It should be mentioned that the basic properties and fabricationtechniques described above could also be applied to a structure withsubmicron dimensions in every lateral direction. Such a structure couldbe called a "tunneling dot" and would be expected to have propertiessimilar to a submicron round aperture. Although its transmission wouldprobably be quite small, its relative simplicity and ease of fabricationmay give it advantages in applications requiring a "point" detector orlight source. In fact, FIGS. 18A, 18B, and 18C can be considered to showthe manufacture of the tunneling dot as well as the tunneling slit.

FIG. 19A is the calculated transmission T(x) through a tunneling slit ofparabolic cross section in which the parabolic shape is 0.5 μm wide and1 μm high. The transmission of this structure is roughly equivalent to aslit whose full width is less than 50 nm. The shape of the tunnelingslit z(x) is superimposed on this plot, the dimensional variables usedbeing defined in FIG. 19B. FIG. 20A is the calculated transmissionthrough a tunneling slit of triangular cross section in which the widthand height of the triangular cross section is the same as that of theabove parabolic cross section (tunneling slit shape superimposed on FIG.20A). In this case the tunneling slit has a transmission profile lessthan 10 nm wide. The dimensional variables are defined in FIG. 20B. Thetransmission depends on the thickness z₀ of the thinnest layer of metal.This thickness, although affecting overall transmission, does not affectlateral resolution. These data show it is possible to fabricate veryhigh resolution tunneling slits using conventional lithography.Equivalent resolution in a conventional slit would require an extremelynarrow slit width, which may be more difficult to fabricate. Thesecalculations are based on a simple ray optics model which ignores theeffects of diffraction. However, the basic properties are confirmed byrigorous calculations based on the analytical wave guide model.

FIG. 21 shows the MTF's for tunneling slits. Their response at highspatial frequencies are excellent, much higher than for normal slits.

The transmission through the parabolic tunneling slit is calculated tobe 7.96×10⁻⁴ for the TE mode and 1.34×10⁻⁴ for the TM mode. These valuesare smaller than those shown earlier for the conventional slits.However, given the decrease in transmission for narrower slits shown inFIG. 5, a conventional slit narrow enough to match the MTF of thetunneling slit would probably have a comparable transmission. Note theTE mode transmission exceeds that of the TM mode; this is opposite tothe behavior of the conventional slits.

Aerial Image Performance

Table 1 below summarizes simulations of the response of a slit to theaerial image for given conditions of illumination and projection lenscharacteristics. The results below were all calculated under theconditions of NA=0.6 and σ=0.5 at a wavelength of 248 nm. σ is thecoherence factor:

σ=(NA at the reticle)/(NA at the wafer). The lens was assumed to beaberration-free. The slit image is proportioned to the square of theforward component of the Poynting vector ExB where E and B are theelectric and magnetic fields respectively of the image. However, theaerial image is represented by the square of the electric field vectorE², since photoresist exposure is determined more by E² than by ExB.This introduces some inconsistency in comparing the slit and aerialimages, because the images created by these two representations are notidentical, as shown below.

Results are given for tunneling slits with parabolic and triangularshapes, for a 120 nm thick Mo metal film with 50, 100, 150, 200 nmvertical wall slits, and for a 50 nm vee slit. From the MTF curves onemight have expected good agreement between aerial and slit images forthe narrower slits and the tunneling slits; however, this is not thecase. The reason is that given above: the aerial image intensity E² isdifferent than that for ExB. One result is that the slit image isfrequently narrower than the aerial image represented by E², aninitially surprising result.

In the table, W_(slit) denotes the slit image width (ExB),W_(A),E.spsb.2 denotes the aerial image width (E²), and W_(A),ExBdenotes the aerial image width (ExB).

                  TABLE 1    ______________________________________    Slit Geometry                 TEM           TMM    ______________________________________    1.  Triangular tunneling                     W.sub.slit = W.sub.A,ExB ≈ W.sub.A,E.sup.2                                   W.sub.slit = W.sub.A,ExB                                   < W.sub.A,E.sup.2        slit    2.  Parabolic tunneling                     W.sub.slit ≈ W.sub.A,E.sup.2 ≈ W.sub.A,Ex                     B             W.sub.slit ≈ W.sub.A,ExB <                                   W.sub.A,E.sup.2        slit    3.  50 nm vertical wall                     W.sub.slit ≈ W.sub.A,E.sup.2 ≈ W.sub.A,Ex                     B             W.sub.slit ≈ W.sub.A,ExB <                                   W.sub.A,E.sup.2        slit    4.  100 nm vertical wall                     W.sub.slit ≈ W.sub.A,E.sup.2 ≈ W.sub.A,Ex                     B             W.sub.slit ≈ W.sub.A,ExB <                                   W.sub.A,E.sup.2        slit    5.  150 nm vertical wall                     W.sub.slit ≈ W.sub.A,E.sup.2 ≈ W.sub.A,Ex                     B             W.sub.slit ≈ W.sub.A,E.sup.2 >                                   W.sub.A,ExB        slit    6.  200 nm vertical wall                     W.sub.slit > W.sub.A,E.sup.2 ≈ W.sub.A,ExB                                   W.sub.slit > W.sub.A,E.sup.2                                   > W.sub.A,ExB        slit    7.  50 nm "vee"  W.sub.slit > W.sub.A,E.sup.2 ≈ W.sub.A,ExB                                   W.sub.slit ≈ W.sub.A,E.sup.2 >                                   W.sub.A,ExB        slit    ______________________________________

In the first four cases, the slit has adequate resolution to reproducethe aerial image (ExB). In the TEM case it also reproduces approximatelythe E² image in the first five cases. In the TMM case, the E² aerialimage is less than the ExB image for the narrower slits, but it becomeslarger for cases 5, 6 and 7. Thus, somewhere between vertical wall slitwidths of 100 nm and 150 nm, we may expect W_(slit) =W_(A),E.spsb.2. The50 nm vee slit is somewhat similar to the 200 nm vertical wall slitcase, because of tunneling through the thinner parts of the slitstructure.

A study of the data which produced Table 1 shows that a vertical wallslit of width 150 nm represents a close to ideal detector, with littlepolarization dependence, and agreement between aerial image width andmeasured image width to within 5%.

Other Applications of the Tunneling Slit or Dot

The expected ease of fabrication and the very high MTF of the tunnelingslit suggest other applications as well. The one-dimensional slitgeometry is suitable for measuring microscopes designed to measuredistances very accurately in a given direction. An example is a systemto measure line widths very precisely on lithographic masks orsemiconductor wafers. It may also have application as a detection sensoron a high density optical disk or magnetooptical disk.

Another class of applications uses the tunneling slit as a verylocalized source of light for creating submicron patterns in thin layersof photoresist. In this case light is provided on the substrate side ofthe tunneling slit, and some fraction of the light tunnels through wherethe metal film is thinnest. A film of photoresist placed very close tothe slit surface will be exposed primarily over an area comparable tothe region where tunneling through the metal film is appreciable. Thusexposure of submicron patterns should be possible. While thetransmission of light through the tunneling slit may be expected to besmall, the simplicity and potentially low cost of the tunneling slit maygive it advantages over other photolithography techniques for someapplications.

Conclusion

In conclusion it can be seen that the present invention provides aneffective technique for analyzing the performance of an optical systemby scanning a subwavelength slit over the aerial image formed by thesystem.

As will be understood by those familiar with the art, the presentinvention may be embodied in other specific forms without departing fromthe spirit or essential characteristics thereof. For example, thedisclosed apparatus and method could be used to analyze the intensityprofile of a laser scanning system. Accordingly, disclosure of thepreferred embodiment of the invention is intended to be illustrative,but not limiting, of the scope of the invention which is set forth inthe following claims.

What is claimed is:
 1. A tunneling device for use at a wavelength R,comprising:a substrate comprising a first surface and a second surface;an optically transparent upstanding structure coupled to and extendingnominally upwardly from said first surface of said substrate; and ametal film that covers said first surface of said substrate and saidstructure, said metal film having a thickness, measured at the highestportion of said structure, much less than the wavelength R.
 2. Thetunneling device of claim 1, wherein said structure is manufactured fromoptically transparent material.
 3. The tunneling device of claim 1,wherein said structure is manufactured from fluorescent material.
 4. Thetunneling device of claim 1, wherein said substrate is a fluorescentdetector.
 5. The tunneling device of claim 1, wherein said substrate isa light pipe.
 6. The tunneling device of claim 1 wherein said structureis an elongate ridge so that the device is a tunneling slit.
 7. Thetunneling device of claim 1 wherein said structure is a protuberance sothat the device is a tunneling dot.